Three In A Row

January 9, 2018

Since the purpose of the exercise is to find three items in a row, we pick up in the middle of the problem with the input already parsed into a list; if you want to work from a file, have a look at the Text File Databases essay:

(define sample-input '(
  ("01/11/2018" . "0003")
  ("01/12/2018" . "0003")
  ("01/13/2018" . "0004")
  ("01/13/2018" . "0003")))

Our strategy is to sort by userid and date, then scan. To make the sort simpler, we “sign” each input record by converting the userid and date to an integer, so the first record in the file becomes 32458130, where 3 is the user id and 2458130 is the julian number of 1/11/2018:

(define (signature x)
  (+ (* (string->number (cdr x)) 10000000)
     (julian (string->number (substring (car x) 6 10))
             (string->number (substring (car x) 0 2))
             (string->number (substring (car x) 3 5)))))

Then the solution looks like this:

(define (three-in-a-row xs)
  (unique =
    (map (lambda (n) (quotient n 10000000))
      (map car
        (filter first-three-in-a-row
            (unique =
              (sort <
                (map signature xs)))))))))

Working from the bottom up: Map signature signs each input record, sort brings together users by date, unique discards multiple appearances on the same date, cdrs makes a list of each starting point in the sorted list, filter first-three-in-a-row discards records that don’t appear on three successive days, map keeps just the first day, map extracts the userid, and unique keeps only a single instance of each userid. Whew!

We use two auxiliary functions. First-three-in-a-row is #t if the first three integers in a list are in ascending order, or #f otherwise:

(define (first-three-in-a-row xs)
  (and (pair? xs) (pair? (cdr xs)) (pair? (cddr xs))
       (= (+ (car xs) 1) (cadr xs))
       (= (+ (car xs) 2) (caddr xs))))

Cdrs is mis-named, but I can’t think of a better name. Not only does it return a list of all the cdrs of a list, but it also returns the original list:

(define (cdrs xs)
  (do ((ys xs (cdr ys)) (yss (list) (cons (cdr ys) yss)))
      ((null? ys) (cons xs (reverse yss)))))

Running the program tells us that userid 3 appeared on three successive days:

> (three-in-a-row sample-input)

You can run the program at

Pages: 1 2

2 Responses to “Three In A Row”

  1. Daniel said

    Here’s a solution in C.

    I’ve assumed the input is properly formatted, as that assumption was part of the problem. It wasn’t specified whether there would be duplicate entries (e.g., a customer appears multiple times on the same day), so I’ve handled that scenario in the code.

    /* three_in_a_row.c */
    #include <stdbool.h>
    #include <stdio.h>
    #include <stdlib.h>
    #define CHARS_PER_LINE 16
    struct record {
      int julian_date;
      int userid;
    typedef struct record record_t;
    int calc_julian(int year, int month, int day) {
      --year; // astronomical year numbering
      int term1 = (1461*(year+4800)+(month-14)/12)/4;
      int term2 = (367*(month-2-12*((month-14)/12)))/12;
      int term3 = (-3 * ((year+4900+(month-14)/12)/100))/4;
      int term4 = day - 32075;
      return term1 + term2 + term3 + term4;
    void parse_records(FILE* fp,
                       record_t* records,
                       long n) {
      for (int i = 0; i < n; ++i) {
        int year, month, day;
        int userid;
        fscanf(fp, "%2d/%2d/%4d\t%4d\n", &month, &day, &year, &userid);
        record_t rec;
        rec.julian_date = calc_julian(year, month, day);
        rec.userid = userid;
        records[i] = rec;
    // Compare by user id first, then by julian date.
    int compare_records(const void* a, const void* b) {
      record_t rec1 = *(record_t*)a;
      record_t rec2 = *(record_t*)b;
      int output = rec1.userid - rec2.userid;
      if (output == 0) output = rec1.julian_date - rec2.julian_date;
      return output;
    // Calculates users that appeared on three successive days.
    // The records array is destructively sorted.
    // Allocated memory should be free'd by calling free_three_in_a_row.
    void calc_three_in_a_row(record_t* records,
                             size_t n_records,
                             int** usersp,
                             size_t* n_usersp) {
      qsort(records, n_records, sizeof(record_t), compare_records);
      size_t n_users = 0;
      int* users = NULL;
      int count = 1;
      for (size_t i = 1; i < n_records; ++i) {
        record_t current = records[i];
        record_t last = records[i-1];
        if (current.userid != last.userid) {
          count = 1;
        } else if (current.julian_date == last.julian_date) {
        } else if (current.julian_date == last.julian_date + 1) {
        } else {
          count = 1;
        // Add user if this is the user appeared on three successive days and
        // hasn't been added yet.
        bool new_user = n_users == 0 || users[n_users-1] != current.userid;
        if (count == 3 && new_user) {
          users = realloc(users, n_users * sizeof(int));
          users[n_users-1] = current.userid;
      *n_usersp = n_users;
      *usersp = users;
    void free_three_in_a_row(int** usersp) {
      *usersp = NULL;
    int main(int argc, char* argv[]) {
      if (argc != 2) {
        fprintf(stderr, "Usage: three_in_a_row <FILE>\n");
        return EXIT_FAILURE;
      FILE* fp = fopen(argv[1], "r");
      if (!fp) {
        fprintf(stderr, "%s: %s: Error reading file\n", argv[0], argv[1]);
        return EXIT_FAILURE;
      fseek(fp, 0, SEEK_END);
      long n_bytes = ftell(fp);
      size_t n_records = n_bytes / CHARS_PER_LINE;
      record_t* records = (record_t*)malloc(sizeof(record_t)*n_records);
      parse_records(fp, records, n_records);
      int* users;
      size_t n_users;
      calc_three_in_a_row(records, n_records, &users, &n_users);
      for (size_t i = 0; i < n_users; ++i) {
        printf("%d\n", users[i]);
      return EXIT_SUCCESS;


    $ c99 -o three_in_a_row three_in_a_row.c
    $ ./three_in_a_row data.txt


  2. Daniel said

    There’s a bug in my calc_julian function above. The second sum in term1, along with its operands, should be enclosed in parentheses. Here’s a corrected version of that function.

    int calc_julian(int year, int month, int day) {
      int m1 = (month-14)/12;
      int y1 = year+4800;
      int term1 = 1461*(y1+m1)/4;
      int term2 = (367*(month-2-12*m1))/12;
      int term3 = (-3*((y1+m1+100)/100))/4;
      int term4 = day-32075;
      return term1+term2+term3+term4;

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